derivative of 11arccot(x+11arccot(1/x))

解

\frac{d}{d x} (11 arccot (x) + 11 arccot (\frac{1}{x}))

0

解答ステップ

\frac{d}{d x} (11 arccot (x) + 11 arccot (\frac{1}{x}))

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (11 arccot (x)) + \frac{d}{d x} (11 arccot (\frac{1}{x}))

\frac{d}{d x} (11 arccot (x)) = - \frac{11}{x ^{2} + 1}

\frac{d}{d x} (11 arccot (\frac{1}{x})) = \frac{11}{1 + x ^{2}}

= - \frac{11}{x ^{2} + 1} + \frac{11}{1 + x ^{2}}

簡素化

- \frac{11}{x ^{2} + 1} + \frac{11}{1 + x ^{2}} : 0

= 0